Recent content by QuArK21343

In my book on waves, it is said that, given a flexible string under tension, a derivation of the transverse velocity v can be given by viewing the string in a frame moving uniformly with a velocity equal to that of the wave itself. The velocity can be found by requiring the uniform tension of...

Thank you, Vargo!

Here is the full passage: "A well-known theorem in riemann's theory of functions says that if a two-dimensional potential v vanishes together with its normal derivative along a finite curve segment s, then v vanishes identically in the whole plane." Analyticity is not stated, but maybe it is...

I found this theorem in my book on optics which I cannot prove: if f is a potential function in the plane, which is zero along a curve and such that the normal derivative to the curve is itself zero at any point along the curve, then f is zero in the whole plane. Can you give me a reference on...

They must be o(||x||^{-m}) but not only that, also all their derivatives must satisfy the same condition (I was in a hurry this afternoon). And yes, you are right, my estimate is clearly wrong. My new attempted solution is this: just notice that it is a limit as n\to \infty of the Fourier...

I see, but my definition of a test-function is an infinitely differentiable function that goes to zero faster than any inverse power. Is this equivalent to saying that it has a compact support?

What worries me is that the last integral I get (the integral of the complex exponential) does not exists, does it? Shouldn't the limit function be summable?

Ok, by summable I mean that the integral over all space exists and it is finite. I don't know if the same terminology is used in english. Also, I didn't write the limits of integration, but they are over all space (let's say over all R or R^N). The dominated converge theorem I have studied says...

I have the following problem: prove that the sequence e^{inx} tends to 0, in the sense of distributions, when n\to \infty. Here it is how I approached the problem. I have to prove this: \lim \int e^{inx}\phi(x)\,dx=0 , where \phi is a test-function. I changed variable: nx=x' and got...

Thank you very much for your reference! By pure coincidence I am also reading Sakurai's book, so I will definitely have a look.

I am reading chapter three of Huang's Statistical Mechanics and I have a problem with equation (3.22). Having discussed the derivation of the classical cross section for a scattering process, Huang moves on to the quantum version of it. He states that in quantum mechanics the fundamental...

Thank you, haruspex, for your link. I'll read it with care (I've had a quick look and seems good). Yet, I still don't see if and why the velocity of heat transfer should be infinite (I mean, is there a way to look at the heat equation and see it?).

So, is it impossible to extract some kind of heat-front velocity directly from the heat equation (as in the classical wave equation)? And why is it so? Is there some way to see that the velocity of propagation is infinite from the equation itself? Also, is there some simple way to estimate the...

Consider a wire of length l. At time t=0, one end of the wire is at temperature T_0, while the rest of the wire is at temperature T_1, T_1<T_0 (for example, one end of the wire is kept in contact with an external hot body, at temperature T_0). After how much time the temperature near the second...

I have had a quick look at wikipedia's pages on student t-test and t-distribution and as far as I understand, your interpretation is very sensible. Assuming that the test to use is the t-test, how should I proceed in practice? Unfortunately my translation is literal, so the problem's statement...